StatisticsChapter 14Factorial designs Factorial design: when an experiment has two or more independent variables.There are several types of factorial designs:Independent factorial design: there are several independent variables or predictors and each has been measured using different entities (between groups).Repeated-measures (related) factorial design: several independent variables or predictors have been measured, but the same entities have been used in all conditions.Mixed design: several independent variables or predictors have been measured: some have been measured with different entities, whereas others used the same entities.We can still fit a linear model to the design.Factorial ANOVA: the linear model with two or more categorical predictors that represent experimental independent variables. The general linear model takes the following general form:Yi =b0 + b1X1i+b2X2i+... +bnXni+ƐiWe can code participant’s category membership on variables with zeros and ones.For example:Attractivenessi = b0+b1Ai+b2Bi+b3ABi+Ɛib3AB is the interaction variable. It is A dummy multiplied by B dummy variable.Behind the scenes of factorial designs Calculating the F-statistic with two categorical predictors is very similar to when we had only one.We still find the total sum of squared errors (SST) and break this variance down into variance that can be...